prob stat: x̄=∑xk where k=1,2,3,...,n?

2nd example: Find the sum -0.31, -0.19, -0.07, 0.05, 0.17, 0.29 via median

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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logic Idempotent law show x=xVx

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Pantun Melayu [Buah cempedak di luar pagar]

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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1st/3parts: Checkpoint 1.1 STPM Math T Sem2

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3 ways: If y=x/(1+x^2) find dy/dx.

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2 ways: diff eq Solve dy/dx=y-1

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2nd/2ways: trig Evaluate (sin^6(x) + cos^6(x))/(sin^2(x) cos^2(x)) dx

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2nd/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via "picture".

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diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable

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3rd/3 parts: Growing patterns

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3 ways: exp trig Differentiate the function a^sin(√x)

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1st/3 ways: Show 1+2+3+...+n=n(1+n)/2 via picture

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2nd part/3parts: Mean of -11,-2,7,...,70 SAME as Mean -11 & 70

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When a die was thrown the scores was an odd #. What is the prob. that it was a prime #?

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U Penn: Show that the following decomposition CANNOT hold ...

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3rd/3ways: derivative (x+1)^(1/2) (x+2)^(1/3) (x+3)^(1/4) (x+4)^(1/5) (x+5)^(1/6)

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2nd/2ways: Evaluate trig integral ∫1/(sin(x) + cos(x)) dx

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JHU: sq root integral ∫e^√x dx

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